{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "23e5667c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "numpy      : 1.23.4\n",
      "scipy      : 1.9.3\n",
      "torch      : 1.12.1\n",
      "pomegranate: 0.14.8\n",
      "\n",
      "Compiler    : GCC 11.2.0\n",
      "OS          : Linux\n",
      "Release     : 4.15.0-197-generic\n",
      "Machine     : x86_64\n",
      "Processor   : x86_64\n",
      "CPU cores   : 8\n",
      "Architecture: 64bit\n",
      "\n"
     ]
    }
   ],
   "source": [
    "import numpy\n",
    "import scipy\n",
    "import torch\n",
    "\n",
    "from sklearn.datasets import make_blobs\n",
    "from torchegranate.distributions import *\n",
    "\n",
    "from sklearn.mixture import GaussianMixture\n",
    "from torchegranate.gmm import GeneralMixtureModel\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn; seaborn.set_style('whitegrid')\n",
    "\n",
    "numpy.random.seed(0)\n",
    "numpy.set_printoptions(suppress=True)\n",
    "\n",
    "%load_ext watermark\n",
    "%watermark -m -n -p numpy,scipy,torch,pomegranate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "1cbdc77a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f0b0f8a4130>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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bao9g8eV2vFrnCL1TShgyzi9j9nglvLjjIB6aP23AQYNzXSieMawQGaivb7t1rR26ibLB/SfJuMdOMvIH9ZBtrj+Kdxra1OdKtEM7nOtC8YxhhchAfX3bLcvPClucjUi7xUJ/QzvaMDPYuS5ERmNYITJQf9925bC1ZilZiAJgEkIDq/JcqW5u73NoJ1zP3eI59pF8CERDwrCNDIkosDS5akkpbi2dhKolpSH1NHzBYwCUNH5w6UR8tPIa3HzFJN3xm2bnqBtSPrPt/GrLNLNJ3VFb2fwwmg0vieIBe1aIDORwudUVPm/vOYbtyyt0w0CpZlPE1T6U2LY2tSE304o3/6Jfnn6pfRzybOlYV9Oi27V5yVX5APTDQlVLSjlPhRICe1aIDFTd3K6GkW6fX12mDAR6XVYsKDSqaWQwSQbW1rToNo+0mARUFuWEvX5mekpIT4qz04P3l12Np28u5lJlimsMK0RDTNsNf6H3c8R1bohaRfHObALu/d4U9efKohykmQNv4WlmE4rtGXCd7VaPKT0pebZ0LJ5jZ1ChuMZhIKIhNNDCW5VFOViz/QC6fH6kmU2oLMqBw+XG63UOvPwn/bdqSm4+P/BSzSG8/PEhvHpfOcoLbNi2vAJ1rR2wZ1ixdGM9PF4JqWYTnqycicqiHAYUShgMK0RDKNJS5L5qYSzvHepRuvcXrKnhPBWKSJKBn6zfhT8+Ol+tZLtlt1N93nX7/LCNTmVQoYTCsEI0hMItRdb2tqSaTVixoFANJtpemGJ7BjbVHmFQoX75/HJITR5OpKVExrBCNITCbTIX/K13VfU+PPfBV1h23XRdL8xdG3bBK3GpMvUvtXeZMqDf3NLZ6WHBN0pIDCtEQyx4kzntt16F8m9labIogEGF+pWXacX3po9Xn1/cnJCSBVcDEQ0zpbflycqZupUaE8amwd9b9I05haLRdsaD3+4+ilXV+7BgTU3YCrZEiYg9K0QjIM+WrquPUWzPCAz7sEItDUBgOlPgOdPt8+O0u4dzVSgpMKwQRSHanW37ur22u37ZddMjDvtwNyAKZhICuy9bTIIu4Gamp3BzQkoKDCtE/bjQeQEOlxsv7jio667vdHsjXp9BhYKtuaUEXr8Me4YVS6rqdHV5gudIESUihhWifkSqnRINbdBRWEQB33gihxWzSeAGhqRz/JsuPFBRAADYuLQMbzUcw6KSXIYUShoMK0T9uJAaFtqgA0Bd9bP5L46w1xcABhUKsbp6HyaMTcNleZlqpdp3Gtq4+oeSBsMKUT/C1U6JljboWERBnafi85+fh6DFmELh+AE8srkB18wYP+hePqJ4xrBCFIXBzgvQBh3t/i1Wi4h75+XjhY9ahqG1lKg+2n9S/TdX/1AyYVghGmbaoKMEF4tJwHMffmVwyyheiQJQtaSUvSqUNFgUjmgE5dnSYc+w4pHNDTh86pzRzaE4UWLP0P0syYCz02NMY4gMwLBCNIIcLjee/eCA0c2gOJEzLg13lE1C5ewJuuOiSYDFJGDLbiccLrdBrSMaORwGIhoh4ZYxE/Wl/UwXXqs7ihRRUPeRAgDJL+ORzQ0AwD2BKCmwZ4VohAQvYyaKVo8kY8WCQtxaOinkMu4JRMmAYYVohCjLmAEgzWzCNTPGG9wiiheiAFQW5eCh+dPU55CCq4IoGXAYiGiEKMuYq5vb8cy2/bplqERA4NujP8zxv726IGRFmT3DCmenh3sCUVJgWCEaQcqHSo9mE8NrZoyHp0dC7WF25Se7cEHFYgJuL8tTf+ZeQJSMOAxEZLCZE8aiJC+DL0YKS4ZgdBOIDMf3R6IRVlmUgzRz4KWXajZh/SeH8FLNobDfqin5BEcTn1/mBFpKehwGIhphebZ0bFtegbrWDrjOdmNV9T6jm0QxRIZ+7kqa2cQJtJT02LNCZIA8WzoWz7Fjwtg0o5tCMUwUgI1LyzhHhZIewwrRCHC43CHVRh0uN1ZuadRdb+aEMSPdNIpBSq+KJAONzk4jm0IUExhWiIaZUrl25W8bcf1zH6uBpa61A17NqiATgJvn2A1qJRFR7GJYIRpm2sq12mqjZflZSBHPT6f0A1hVvdeIJlKMsogCioM2MSRKRgwrRMNMW7k2uNqoX9Zf1+cPzFOg5GYRBZhNgFeSsXRjPWpbXNy0kJIaVwMRDTOlcm1da4dabdThcuPFHQfhC0orqWYTHrt+Bv5lK3tYksXU7FE4fOoctM8ESZLVeSser4S7NuyCV5K5aSElLYYVohGgrTpa2+JSP3wUZpOA+743BfMLL8JPq+qMaiaNEAFQw8mhU+eQajbBK/nVnjY/Ar0rXklW/w+cH0ZkWKFkw2EgohHkcLlDgspNs3Pwx0fn44nKS+Ds9KDbx/JwiU5A4O+u6Pb58cDVBbD0jgFaLSI23TMXT99cjE33zI04jEiULNizQjSCglcAAcAHe7/G4zfMBBCY35JqNjGwJDg/gElZVlgtIjxeCVaLiNvL8nB7WZ5uuFARPIxIlGwYVohGkD3DquvWBwLfqpWu/TxbOrYvr8BrdUfw8seHEJRrKIFkpqeEDSHhwgg3L6Rkx7BCNEIcLjeWbqxX5yEICOy+HNy1n2dLR2Z6CoNKAkszm1BZlMMQQhQlhhWiEaKtt+KVZDxZORO20am6FULVze0AgNPuHiObSsPEbAL+/vqZalAhougwrBCNEKXeijJHQfuB5XC5sWBNjTpXRTQJMAuAT9ZvakexbWr2KBw6dS7sZRZRwKZ75qK8wDbCrSKKfwwrRCMkXL0VRV1rh25SraSpvyKaAD/TSswKXoasZREFPHHDTHzm6MSkLCsmZlhHvH1EiYBhhWgERZqjUJafBbMpUME2mJdBJaYJAjA3Pwu1hzt0x2+anYO7yifjp1V1ahDduLMV25ZXcAiIaIBYZ4UoBuTZ0vFf95aHLbWfajYhzRx4qYoCa/HHGr+MkKAiCsBd5ZND6uZ0+fyobm5n6XyiAWJYIYoR5QU2fLTyGjxYMRVmUyCUWEQBv15ahm3LK/Bk5UyYBP0SoRSRL+FYJMnAkqo62DOsSDWf/xuliALWbD8QsgM3EfWNw0BEMSTPlo5pF41R9wzySjKcnR6UF9hgG50aMiR0z7x8HO3wYGtTuwGtpb50+fxwdnqwfXmFusoLAFZV7wPA0vlEA8GvZUQxJtwuzQ6XG66z3WGHiSZlWblTc4yyZ1iRZ0vHAxUFqCwKlNdXeloGWzrf4XJzGImSDntWiGJM8KohALj+uY/h8UqBDzrJD0kGLCbglT8dUiflWkQBV0/Lxof7TxrYetJydnoABAKG8jdMM5vwZOXgaq1o74c7MFMyYc8KUQzKs6Vj8Rw78mzpumJy3T4/HrthJp6snAm/rF895JVklE21wcxelhFnS7eEHNP2nGj/hl0+P2yjU0NCRjQ9Jtr7UYaRiJIBe1aIYpy2mJyyKuiI61xIOX6lhHtlUQ5eqzuCHftPYt/xbw1ocfJxub26n8umZGHFdYWoa+1AW6cHB098q+4JFW74J9oek+DCgtyBmZIFwwpRjFOGhaqb2/Hs9gPqBE2ta2aMxy9+UKR+wM0vvAiv/OnwSDeVepXlZ2Lpxnq1F0RhMQmoWlIaEkTC9ZhE2tCQOzBTMmJYIYoxDpc77E68ttGpupodCrNJ0AUVh8uNn6zfpa4o0mLp/pHxwd4TIUEFALx+GW81HMPE3om3ioH0mHDzQ0pGDCtEMSTccAAQ+OZtz7CqH2gKZb+Z4NL94YIKAJgEQBAEXTl/Gnr7jn8L0RT+PG+uP4r/3nMMG5eWwdnpUUNpcI9JuNBKlKwYVohiSPBwQHVzO5774Cs1vDz1o9lYuaURXkmOuDFeWX4WUs2msL0wPhmAfP4D9LtTsiAjtAIrXbi+AmGXz487XqmFXw4sZV6xoBCVRTlYPMcOgKt+iIJxNRBRDAmusQJAF14+PeSCV9IXjAteRZJnS8f23oq3d5bloSB7VMTfV9fawaBiECXLdPv8WFW9D99/dgdqW1wAuOqHKBh7VohiSLgaK9qelUUluXinoU392Z5hDfsNPM+WjsqiHCxYUxO2h0URvKIICAwVcZRo5HklGXdt2IUPV8znqh+iIAwrRDEmeAJl8FyG95ddjdfqjuBohwc7DpwI+w28rrUDrrPdfQYVAGF3emZQMY5XklHX2oHFc+xc9UOkwbBCFOOCw0tbpwcv1RxSf04RBfT01u/Q9rRYohjkvbEoB2PSLHitzoFwGcViQsh+RDQ07izLw5bPnLpAqe1F4aofovMYVojizKbaI7qfF8yagGtmXoSy/CzdXIdoQsY7n7fDYgIsogk9UugNFn4nh5skDrGC7FGYOzXQW/Lr3hVB9gyrbmUQVwIR6RkeVp5//nm88MILumPZ2dnYuXOnQS0iil0OlxvbvzyuO3ZX+WTdiiBlroPS49KfQKgJn2xcZ7shAGF7XWhwDp06h5ZT5wAEesXumTcFrrPdKLZnqBVvlYJyXAlEFGB4WAGA6dOno6qqSv1ZFEUDW0MUu6qb23UB5M6yPF1Q0U7QtZgEvFTTgr0XUHKfK4WGnjb49UiybkgPgFqWH+i7mi1RMomJsCKKIsaPH290M4jiTqSS7G2dHtz2cq0BLaIL5Q3qDbNnWA1qCVHsiImwcuTIEcybNw8pKSkoLi7GihUrMGnSpAHdhySFlraOZ8rjSbTHFQ9G8tw7Otyobz2N0vxM5GX1/+154ayL8Oz2A+j2+ZFqNmHhrIvUdir3lZuRhn/Zune4m04jZM/RDpTmZwz77+F7jnGS9dwP5PEKsiwbOhxdU1ODrq4u5Ofnw+VyYe3atTh06BD+8Ic/IDMzs9/bS5KEhoaG4W8o0RA7ftaHFdtOoVsCUkXg2YXZmDC6/+8Px8/6sPeUF5dkWzBhtBnHz/pQ6+zCG81n4eXkkrgkCoAgAz4AFgGAcH6CdIoJWHN9dM8NonhUUlLS7/QPw5/9FRUVup9LSkqwYMECvP3221i6dGnU9zN79uyEmusiSRKampoS7nHFg5E697/77Bi6pVMAgG4JOJeeg5KS3Kh6W2b1XqdrbBpWvv1Z2E3zKH5IMvD4DYWwjUpFbkYaXq07inebAhOpe/znnxvD2ga+5xgmWc+98rijYXhYCZaeno7CwkK0trYO6HaiKCbkHzlRH1c8GOpzH7wctXxqtq5KafnUbBzr7MaNv9oZshJEe1sA6nW0kzEp/ih1bCyigMsmBf62d23YpfubWi0i8rJG4a2G9hFZysz3HOPw3EcWc2Glp6cHLS0tmDNnjtFNIRoykTamC65SumW3U1eR9sUdB7GoJFe3lHXZddPP11JhUIlrPj9gNgUC50/W74Isy7otEG4tnRTy9+dSZkpGhoeV1atX45prrkFOTg46Ojqwdu1anD17FosWLTK6aURDJtzGdEqFUu0Hj3ZPGADYXH8Uv9/thNd/filrp9uruw7FLxmAr/dv6wva58AiCnho/rSIzx2iZGJ4WDl+/DhWrFiBzs5OZGZmoqSkBG+++SZyc4d3fJZoJJXlZyHNbEKXz480synixnRKb8uLOw5ic/1RAFCDimLDzsP49dIy/E9jG16tcwx722nkmU0CNt0zVw0l3NSQkp3hYWXNmjVGN4FoRMhB/48kz5aORSW5+P1nzrDDPN0+P3YcOIHXGVQSlmgSMLG3vkq44UKiZBPFVmdEdKHqWjvUDeu6fX51d+RgDpcb62pacHfQJMtgL9UcilAgnxJBt8+P6ubzezLl2dKxeI6dQYWSluE9K0TJQDsXJVJXvnYSLtFpd0/Y49zkkJIRwwrRCIimK187kZJo485W3FE2WfdcibSqjCjRcRiI6AI4XG5s2e2Ew+Xu97pKVz6AsLdRJuECQKrZhAcrpuKaGdwzK1l1hRkuDLcyiCgZsGeFaJAG8y23tsWlFv1KM5uwfEEhiu0ZcHZ6YDEJ8PnPz0S5o2wy9jhO46P9J4f7oVAMSg2zaiya4USiRMSwQjRIA61/4XC5ddVJu3x+rKreF/a6yiTcrZ+3DX3DKWZMzx6Fr06dC3vZigWFIc8nrgyiZMWwQjRIA/2WW9faEXXFWYso4OP9J9irkuAiBRUAKLZnhD0eXEiQKBkwrBANUrhvuX2t1LCYBN3PZgHwhckuogBIkox3Pm8PvZASlmgSIGkKADY6OzExw8peFCIwrBBdEO233P7msHx6yKW77fVFObjUPg5Pv79fV6VWBlhDJckIAG69wo4tu53o6e19e2bbfjy7/QC6e6seb1tewcBCSYurgYiGSH8rNRaV6LeQWDjrYhxxnQspp+/n3oRJRwbwWt1R3d++R5LVQoJdQUXiiJINwwrREFHmsAAIO4elvMCGf7+1BMpo0N9vacQbvfv/EAGBzQwtYuAJYua7M5GKw0BEQ6S/lRoOlxvbvvxa/fbcE+VkW0oeKaKAq6ZlY+aEsagoHI+fVtWh2+dHqtmEyqIco5tHZBiGFaIhFGmlRqRS+mYT4OMElaQnmgTceoUdr9UdxUf7T+Kj/Scxc8IYLL0qH0c7PLirfLJublS8TLqNp7ZSbGNYIRoB4Urpm00CrpicidrDrEKa7CS/jIMn9cuYV7zZCEkO9L59sPdrbF9eAQBxU25fG9AtooBN98xFeYHN6GZRnOKoKNEIKMvPQmrvJASLKRBUfH6ZQYUABOY43VmWpzumBBXgfJHA4EncL+44GNVWD0bQttUrybhrw66YbSvFPoYVohEiaP7l45If6nXT7By8v+xqXDw2TXc8RTz/jFFK72tDLwBsrj+K65/7OCZDQFl+ljpZGAgEFu5lRIPFYSCiEVDd3I6u3skpwUuVKbldah+HPFs6XtxxUHd8wawJuNQ+DgBQWZSjFh0Ugm4fzVYPIyV4jsqme+aqW0wMdC8jznchLYYVomGivNnaM6xYs/2AetwEFn2jAFEIRA+Hy40rp9qwWbOU/a7yySFzPOpaO9TQq4iVDQ3DFUUsL7DhwxXzB1wjZjCbhFJiY1ghGgbBkwu1ewIxqJBCkmWsqt6HX763D8ozxCQAP7/xEjg7PXC43LoPae1+VKlmE1YsKFR7XUZacM9HXxt7PvfBV/B4JazZfgDLo2jzQDcJpcTHsEI0xBwuN17ccVA3uTB43xciLe0eUX4Z+L/V+yD55ZBehVjZddnhcmPhmhp0abYCiLSxpzZ4KDuNP/fBV3h/2dXq5fYMKxqdnQACQ14D3SSUEh/DCtEQCldPxWoR8dSPZmPllsaod12m5KYE23C9CrGw67J2DpayFcADFQW6IAUAW3Y7Yc+wIs1s0g1febwSqpvb1R4XrWe3H8D25RUxEcoodjCsEA2h4HoqZVOysOK6QpQX2PDViW/xwkctBraOjCYAGEhcDderoJ0L5ez0DOrDfKgnr55292DLbifK8rOweI5dF9pTRAF+Wf+olW0pgoMKEFimXd3cDtvo1Ijt4+Tb5MOwQjSEtN3XAFB3uANLN9ajakkpXmRQSXrKvlDhOthMgn4Ty2tmjMcvflCk+zCO1HOnHSrq74N8IJNXI91XZVGOuiN0iiigamcrun1+WC0iqpaU4q2GY2obg7eVuLV0Eh6aPw0A8PS2/SG9jWYBWLP9ALp67y+4fZx8m5xYZ4VoCClzCm4tnaQe83glvNVwbEDfqCkxSTKQm2ENOV42JQtrbimBpfcd2WJCSFABwldC1u7wrXyQr/xtY8T6K33tDn78rA+/++wYHC53n/eVZ0vH9uUVePrmYtwzb4q6O7THK+En63fpVjUFu3KqTX1c986bErIU+zu549Qho3C7l/e3uzklJvasEA2xPFs6Hpo/De80tKnf/haV5OLtPcfUN3UuX05ejtOekGN1hzvQeLQTJpMJ8PshmsJ/jwzuuQMQcTJrpFU0wZNX7RlWbNntRM7YFKzYdgrd0ilYLSKWXTddd1+v1zng6HBjUpYVd5RNRlunBx/tO4FtX+iXJWsLHhZkj0LLKf02Aiu3NOLisWnqJo0WE+DVvBiEoPRiMekPcPJtcmJYIRoGwas2AOC6Sy7G1qbAGzuDCgXr1kxA7fL5sfq9fbjUPk63zFf7vAo3Z6WvD3LtkI5yHxaToBZt0w5DebwSag+5dO1bW3N+GPPlmkMInW0S6tTZ7pB5Ol5JxqbaI+rj9fqBO8omof1MFz7afxINR8/o7mPllkZclpcZcyuiaGQxrBANE2XVRrh5BgOdaEnJQbvEfWtTO7Y2taurY7Qf1pE+oCN9kIfbVLAsPwvff3aHOmckeGX9R/tPRmxnNEEFAM50+cIeH2c1B/2cErKRo8IryXhxx0E8NH9aVOeAEhPnrBANs+B5BiYwqFB4kl8OmcOhbGIIBELHlt3OPvcCyrOlY/EcO4DA0uHaFldI3Z+7NuxCdXO7YUvpJ9tGqXsfmQRg/SeHUBe0qaf2PGyuP4qFa2picg8kGhnsWSEahEirJMId13bNi0L4lSBEiuCnh8UEnHH34AcvfIJ97d+iRwq/SkartsWlDu+E45VkdLq9SBGFkNU6I2Fv+zfq7/XLoSuGgNDzoK3nwqXLyYdhhWiAIi2djHQ8z5aOqiWlfX54EEUyfnQq/mXrXt0x7SqY4A/t2hYX7nyltt9QnJFuwYJZE9R5VCPp7Ya2Qd9W+zozessBGjkMK0QDFGnFRV8rMZydHgYVGpS2b7rDHreYhJBw3NbpwZ3rd0XVe1dsz0CxPcOQsDJYxfYM3eusW1O+v2pJaciEY/bAJA6GFaIBCrfiwuFyw3W2Wy0rHrwSwx6mtgbRhdj25de6cFzd3I5fvr8PUtBSM4sJyBlnDVkyfecrtcizjcLkLCuOdIQup45FOw6cwP7j34YMp3q8ktpzqRSma3R2qoXr2AMT/xhWiAYo3LJkbbf0k5UzQ94UlU3aiIaCCdDVN0k1m3Da3QNfmDXxXj8wMSM0rEgycPhU+BU4sURZOWcC8FLNIfW4KAgQBBk+P3Q7m2uDi6I7aAPFvgILe2NiE8MK0SBol05u2e3UdUvbRqfq3uRqW1z45Xv7DGknxTezoN+RWeEH4NcEkxULCtHp9ka8n7bOrqFv3AhRHn5wDpNkGZABUQCeuGEmnt52ILA02yREHHKNVChPwVL+sYtLl4kukDIsBIRuPOdwuXHXhl1hP3CI+hPN88ZqEVFsz8Arf4q895TjdOIu+ZVkYFX1PlQtKcWTlTNDKuACgZ4XIPzGkFos5R+72LNCdIH6qqhZ19rBibU0bEQBWHJlPhqdnbqS9cnG55dRc+AkCi4aHbIM2moR8dSPZuPTQy4sKsnts6eEpfxjF8MK0RCIVFEz3F4uWtqKpUQDJcmBMviiKUx3QpJ5e48TT1Reor7eTAJwW+kk/KA4F0s31sPjlfBOQ1ufQzvB2xkoPSscCjIewwrRMFLe/Kqb2/H/3tunW8Fw0+wcXGofh9pDrj5LmxP1h4EXaP+mG49sbsAPSybi7YY2+GXgtbqjaD/T1e/mjlrKZZy7ElsYVoiGWZ4tHbbRqbqgYjYBH+79Glub2pFq5tQxoqESXHBO+0Wgr80dgfMF9qLZvZpGFsMK0QjQDgdZRAH3zZuq7mLb7fPju1Oy8OfDnMxHNFxuLZ2ERSW5ukmz2pIDAqDWSKpaUsq5KzGGYYVoBISrzbLx01b1zbA4L4NhhWgYXTnVps5dsVpELLtuuq7kgMLjleDs9EScNE/GYFghGiHBk3CDw8uGTw4bsqkcUTL49JBLN7QDQO09Ce5ZUQIKQ0rsYFghMkjwm+EHK+bjpZqDeK3uqIGtIko8VouIRSW5eHvPMbX8fmVRDiqLcsLOWWFIiT0MK0QGCi7t3X5GX2k0LzO0TDoRRW/86BQ8f/vl2HHghLpqKtxCb/akxDaGFSKDBJf2rlpSio8P6Jcwz5uejcMnz3E+C9EgPVhRgLs37NINsXb5/KhubsdzH3zF5clxgmsmiUaIw+XGupoWrKtpUXtUtGPobzUcQ/CUlS27nbhu1sUGtJYo/t1VnofPHJ1h54KddvewtH4cYc8K0QhwuNxYsKZGXXWwZvsBbFxaplseuagkF7//zKkrz98jyVhVvdeoZhPFtVd3ORCpXl5megqXJ8cRhhWiEVDX2qFbHtnl84ddHrnpnrm485VdgR1le/mSeM8XogsRKahYRAHF9gwuT44jHAYiGgFl+Vm6SrVpZpP6Brl4jl19oywvsOHV++bC3LvXS4oogAVuiS6c9mXklWTctWEX9jhOAwDaOj3YstsJh+v87tQOlzvkGBmHPStEIyDPlo7tyytQ3dwOAKgsyon4TW5ihhV/f/0M9Xp7HKfxyOaGkWoqUUIK7qD0SnLI60qZaAtwb6BYw7BCNELybOl4oKKgz+sErxCqLMrB8W+6+rwNEfXPJEQeFlJ4vBKqm9thG53KvYFiDDuYiWKEw+XG6vf2cYUC0TCIdmPqZ7bthz3DCqtFBBC6+SEZgz0rRDEgeLUQAKT2zmsBgF++vy+qibYmAbg0dxwanGeGq6lEcctsCkxYt5gACAK8kgxRAOYXjseHvbsz90gyGp2dnHwbYxhWiGJA8GohAFixoFB9k/yve8tx+8u10H45LLaPw3cLbDja4cHWpsBcGL8MBhWiCG69Ig+XTc6EPcOKHQdO4JU/HYbPL6Pmq1O663W6vaxoG2M4DEQUA8KtFqosylF/Li+w4blbS3S3ebLyEjxReQkev2EmLGK4AuKxy2oR8Xf9zN8hGmpbPnPCnmHF0o31eKnmEHy9Y0M+v6yuwAOADTsPcxVQjGHPClEMiGa10N9clouLx6bhrYZjWFSSi/ICm3rbTffMxV0bdukKysWiFFHAowtnqEHs5T+1sI4MjZhunx+rqveq88K0rpicidrebS26fX68uOMgHpo/jb0rMYJhhShGRLNaqLzApoaU4OMfrpiPutYO2DOsaHR24nPnGXV4aCh8f+Z4fLjvZP9X7MM986bANjoVQODx3ve9qXip5tBQNI8oKo0Rhklrg/bf2lx/FP+95xiWLyjUfXkI3nyURgbDClGC0I6xlxfY4HC58cd9J3TfIi2iMKjel1Szqd/VFD+4NAfvfB45HJkFYP2fDsPrl9XaFXeUTcbLHx8K2ROJyChlU7JQ1xtcunx+rKreh+c++GpI668w8Awc56wQJag8WzreX3Y1nr65GG/cX46/qyiALIemgoy0yN9ZBADXzBiPXy8tw4wJY/r8fd92+/q8XJIBb2/i4bJsigVmE/BgxVSk9c4Xs1pErLiuUF22rFCer8Gbjw7mOazUUlr520Zc/9zHnBsTJfasECUwpbfF4XLjlU8OhZ0f0tkVOWTIAD7afxJ/bnFh49IybPjkcNgdbNF7PUVKbw+O9praf1tMAsrys1Dd3M5eFTLM/d8rwO1lechMTwFwfq7Y+8uuRnVzO57dfgDdPr+u1sqFbn4YLvAsKsnp51bEsEKUBOpaOy5o8m2Xz49GZyc+WDEfL+44iM31RyNe99bSSXho/jS0dXpwx8u1IWXOAeDe700BECjARWQEUQAqCserwzrKajwlsDxQUYDKopyQ4ZoLrb9Slp/F3Z4HgcNARElAeYMEAm/S/3jTJXiycqba/R2tPFs6Hpo/Tb0viygECmz1SjOb1BUU5QU2PF45M+Q+Us0m3FE2GdXN7RF7aYhGQqOzU+3l6O6dn6IdmgneaDTSMSD6jQ+1w7Pccyh67FkhijODmZyXZ0tH1ZJSdXnz09sO4P1lV6OyKAev1zmwtqalz9unauq+KG+2ShsAhF1yrbxpp5pN6Pb5YTYJuO97U3BH2WQAwJrtBwb+4ImGiJKTlV4OxWD2Agre06u/EBJtwTlOxD0vJsLKq6++ivXr1+PkyZOYPn06/uEf/gFXXHGF0c0iijnRvClGeoNzdnrUoSDlDXnxHDser5yJisLxeKvhGK6caoPXL8OeYYWz06P+P/i+gt9sg5dca9uZIgrqKqRff3oE8wsvwlsNx9DFAitkIGWj0GJ7Bn6yvladz5Wm2eYC0L+eAIR9bYWbh3Kh4SL4tV61pDTsazFZGB5W3n33XaxatQr//M//jMsvvxxvvPEG7r//fmzduhUTJ040unlEMaW/N8W+wkxfY+WR6rcMRTu1Qz0erxQXxesosZkE4KdXTkZbpwebao/oJp4v12xzoX09pZpNEBCYv6W8tgCotY0GMg8lmh6T4Ne68roJ/t3JEl4MDytVVVX48Y9/jJtvvhkA8POf/xyffPIJXn/9dTz66KMGt44otvQ3Oa+vMBM8fDOcb3Dadmrf5Adb54VoKPll4KWaQyEFCVNEQbfNhfb1pN27y+OVsK6mBW/uPqoGiOCej0iBJNwXityM1JA2al9D2teNxyvh9ToHNn7aGvZLSTQ9QfHI0LDS09ODL774An/7t3+rO37VVVdhz549BrWKKHaFCxzaN6f+wsxIbc4Wbl6L8g10SVUdh4AoJimFD5XXlMUkRAzYr9Y51H97vBIanZ3qcKh2F/VUswnbl1cACMzt+tx5Jqqly8o8M2V49vHffa6+brTbVGi/lPTXExTPgcXQsHL69GlIkgSbTd/9nJ2djZMnB1bWW5JC93qIZ8rjSbTHFQ9i/dznZqSqb26HT36LG3+1Uw0n7z58Fd59+CrUt55GaX4mcjNSDXsc2nYCUP/9yPenY/X7XLJMscfnl/Hqrlb85s+OsPsH9eWX7+/DRaMt8PqBPUdOqz0x3T4/1u74Cr/f0xays3qq2YST33Th8MlvAZx/z3F0uPHeF8fx3AcH0e3z452GNvz0u5Ox7k+He9t5vhq11SJiTt44SJKE2kOnIvYE1R46hdyM3MGdmGEykPcmw4eBAEAQ9DvGyrIccqw/TU1NQ9mkmJGojysexMO5/6jVo/uW9ruPG3FNvhUFJqDDcRIdjn7uwAB5Jh9SRaBbCswd6K+MP9FwEaAvVggA9QeODTioAIEAsfy34d8z3qh3hvweIBAoVr+/H2u278ea67OBpiYcP+vDim2n0K1pgscrwd15Un3dpIrAP8zLwEm3H5dkW9DhOIAOBzDKff61lWIKPMCe3uuPcrejoeHC9vYykqFhJTMzE6Io4tSpU7rjLpcL2dnZA7qv2bNnQxTF/q8YJyRJQlNTU8I9rngQT+c+K8+N9Q3ne1Z+fHUx8rJiv6t31qzAN8c1279irRUyhCgATy+ejSfe+kLXC9F80osUURjS56Xc+/si3WWPH6h1duMfb74MLY3H0S3pPxOtFhH3LLwc9yyE2msKBP49Kz9T95qfNcsdcp3SoOvECuW9NhqGhpWUlBR85zvfwc6dO7FgwQL1+Kefforvf//7A7ovURRj/oNlMBL1ccWDeDj3U8aPGbFJs0NBO79m/Bir7gPBbBLgYzcLjRCLaEJOxiisWFCI2kMudbuIHknGTbNzdDuWm4CwlZgHor/sc/h0D0RRRPnUbHXeWZrZFLLr85TxY3RzUyyigE33zFVX800ZPwZTxp/fx0v5d7zXbDF8GGjp0qV47LHHUFRUhMsuuwybN29Ge3s7brvtNqObRhQXRmrS7IUKVzdCOxm4akkp/m/1XnzuPGN0UykJdPn8uP3lWsgIDEeaBcAnB+aRLJx1sS6sDIfs0Sk4dbZH/fkTZzf+99vNyM8eHbGmihI4XGe71aEqryTjrg278OGK+RHfBwZatC4WGR5WbrzxRpw+fRr/8R//gRMnTqCwsBD/+Z//idzc2JoIREQXJnhZtbPTo/YKKcXnln43L+K4P9FQUzo7/PL5nhNZBl6v00/2Go61a9qgoni93gkgsIT6g97w4XC5Ud3cDofLjc1/ccDnDwQq7SolrySrO0CPVNG6kWZ4WAGAO++8E3feeafRzSCiYRRuWbXyhrlwTQ26fH6kmU1YMCUN2w93GdxaSlY9kh+1hzsMboOMf36nGT8sycWKNxtChpC6fX7cWZanWz5tMQmDKggZL2IirBBR4otUlK66uV2tH6H8n/NXKNl9tP+kOo8mmNkEtJ3x6I79R01LTBSEHC4MK0Q0YsLNrznt1neHf3i4CzfNnoD/aTo+kk0jigsCAJMghASZ/ce/Vf+dGrS/ERA/c9siGdj+8EREw8wPoPoLBhWiSPpbVr0iaH+jLbud6i7o8Yo9K0RkGIfLjY07W3XHRAEIrsafajZh8eV2dYIhUbLqb3DUbBJw2t2D2hYXGp2dWLP9QEKU3GdYISLD1LV26PYJunH2xZib1YOnPv1G3d9kxYJCFNszsHRjPXz+oal5kUhSRBMWz8nFa3VHjW4KGUxAYMuAcJs0xusqIAXDChEZxp5h1f18Z1ke0r45incfvgq7HWfUyYBbdjvVyYMMKsCVBVn4S+tp9EgyvFLgjASvDqHkEm7rAK1w81jiCcMKERnG2alf0XCsswsFJiAvK11XhVO79DLVbILkl0NWCykT8OItzBRkj0LLqXP9Xu//u6YAda2ncWdZHrx+GZ+2BJbXygBeqzsKiwkRdwimxNffX/26Sy4ekXYMF4YVIjJMcP2H0vxMdDhCl2vm2dJRtaQUbzUcw6KSQMFIpfqoel9TsgyvjzEY4YKKAMCeacWYVDMuHpeGH5bkwuuXccsVeWqhsOC9Zrx+4MGKKSHd/8liTIqIb3tic6f0kTR+dApOhik4t7WpHX/cdyJu560wrBCRYYLrP+RmpKo7RWv3MgGApRvr4fFKeKehDe8vuxoPVhRgbU2Lel+X5WVit+P0gHsWYuVDTtuNLwM4ejrQ63Tw5Fl82uJCd+8kSaUU+z/ceAn+Zete9fYpooBvPN4Rb3esiIW/YSwIF1QUHq+E6uZ22EanRizlH6t1WBhWiMhQ2voPkhT4wHF0uHHjr87vJr3suum6glcv7jiIRSW5qNp5GF0+PyyigJkTxuDeeVOw/pPDUQcWswBMvWg0GmNgP6JILQ4sUw1c6vFKuGvDLnglGVaLiH+/tQTbvvwak7KsuGTCWPzif74YsfZS/EkRBTy7/QC6fX6kiAIeXTgDlUU5ABDzewexzgoRxZz61tO6cAIAVsv5HbA31x/F0o31WP3jS9V5Go9sbsBLNYdgEgT8XUVBVG9u3yscj3uumjIcD2HQRCHwoRKOdk6Kxyvh00Mu3FU+GQIEPLK5AR1ufc/KxLGpGJMa2zuH0/AZlaJ/FczJy0R37+q7HknGqup9uP65j1Hd3B5S/TbWMKwQUcwpzc9Uw4nVIqKyKAdVS0ohms5/iHu8ErZ9+XVIL0q3z4+MdAv+6tKcqH9fiX0cwseDkSfJwL3zpuKm2fr231o6CZvumRsS2m57uVY3HKZ16lwPvu3m8EiyOtejn26uBJJwx7Svt1hcNcRhICKKOXlZoXuZ1LV2QNKsALKYBGz/MrTSrdkk4Jlt+/ut8gn0vf+KkTbsPIxfLy3DH/edgMcrwSIKWFSSi/ICG95fdjVe3HEQm+sj11URBOD20kmsvUI6DWGGO5UvA5VFOTE9Z4U9K0QUk/Js6Vg8xx6ycywQGA6593tTdIHkjrJJsIiBDRDDBZVp40cNqh0WUcA1M8b3eZ2C7FGYOWFMn9fRutQ+rs/Lu31+ODs9qFpSqg793LVhF2pbXMizpeOh+dN0PSxAoDicoPn3D4pzQ65DpHiwYiqevrlYnZ8S/HqLNexZIaK4ELxyCAB+/ekRdVLgZNuoiBNrLSbgcBS1TJTdnkVBgCQH7ssryUhPMSPVbFLH+7VSRAHHOj26Srwhv18UIPll+OXAN9l/qLwEP1lfG7J1gPL7la74utYO9TEpgeXDFfN158KeYUWjsxOfO89ga1M7gEDYaXR24keX5cZlobj+CpxR/1JMQE+Ep6TVIuKOssm6/YNiuVcFYFghojgSvHNscHh57oOvwo7Le6OoFJciCvjNPXPR6OzEM9v2Q9LczdamdqSaTXiyciYmjE3Dyi2N8EoyLKKAm+dMihgIlFooJkHApvvmwtnpUT8Q/uvecl1gSTWb8OulZbrrAPpJtV5JVkumK/85XG51Wbf2sTy9bX/cFoibMWEM9ml2EaaBixRUzCYBVUtKdUGlr5VAsRJkGFaIKGY4Otz4qNWDrDy3roJtJJHCiz3Dik21R9SeBgC6Imrh9hfqkWQ4Oz2wjU4NO4yk9Kp4/bIuPGz+S99BRbmts9ODxXPs6i64ZflZ+OOj16C6OdDGyqKckA+DPFs6Nt0zV7dcOXjyY11rhy6oFNvHofnYGUTKKWVTsnD9rIt1NVoUsbLvUnBQUXqc6ML5/DJqDpxEeYENgP75E7x/UH9BZiQxrBBRTHC4ztdWWd+w84LeGCdmWPH4DTPx4d6v0eXzI81swpKr8tXqrn4gpAKsRRTUIKBU1TWb9DtAn3b3oLIoR708uLz9gxVTkZmeAgAotmdgSVWd+vvL8rPCvvk/UFHQ52MpL7DhwxXzI3671VYBBtBvzZgV1xWGbHMABCYs/68rxuA/95yDxyuFnJ++aEOOWQgM4fR325lBvSc/KM7BHz5vhzaTFNvH4bsFNswvvAg/Wb+LgWWIvPynFtxeFqiGbM+wqs/j4DDcV5AZaQwrRBQTLuSN0eFyo7q5XS14pQSBbcsrIs5xeepHs3XDOZvumav+Pm0Pzd0bdqk9LRt3tuKOssm6y5UhmHDzALQVacM9xhd3HMRD86f1+ziDe5CCL4tmhdA1M8bjgasLUF5gg8Pl1s3BsYgCNi65AmnfHEXZ7Bl45/PjOPFNV9QrpdbcWoLj33ThtLsH6z85DF8/ScUiBmrhPP67z9W5Pu80todcr9F5BvuPf4vM9BTcWJSDdz5vi6o91DefH1i5pRHXz7oYT723T30NaIeHgNDtMIxc0sywQkQxYbBvjNreCoUSdoJXNwQvh754bJq635DSLQ7ow8GjC2dgVfU+AECXzx9yv8H3qahr7VDDQHfv7YJ7QTbXH1W3D7iQb6zKCqF3Gtrg8UpIM5vw/Usu1g2D3XTpRPUx5tnSsWJBofq4vJKMz4+dQZ7gw8q3Pwv0GgWtFU0RBdxQNCEkVAgCsOuwCw9WTEN1c3vEeTImAD+/6RL1w/GJ3zfpersi6fL5sap6H5euXqDgnrK6wx2o0+yl5e0dBtUKntTOOStElPTybOl49+Gr8LuPG/Hjq4ujfmMMnrMBRC5spQ0h2ompfQWGyqIcrNl+QDecE+k+tcKFr3C9IEPVvR5utZRSpyXc+dA+LgB4ZtsB/NX0Ueq5VCYli0KgIN0PinPx06q6kN8ry4Fdn3/7l6MQhMil9SpmjMe49BRdBd7M9JSoh5tiYS5NPOvvHFtEAfYMqzqfSnk+9tWrN5IYVogoZuRlpeOafCvysqJ/c9SGgjSzCcsXFIadrBpsIMNOwcM50Yj0rTS4F2Qou9f7Wi0VbvLuck3vis8P/M+BcyFLtCUZuHxyFpydnrBLtxWBcHP+DJUH7YI9c8LYkABXWZSDCWPT8Mjmhgt74HRBRAG4Ii9THfI0ejJtOAwrRBTXBttVHe2wU7jhnGh/R6RvpSPVvd7ft+LKohzdEmdJBq6/ZDzyskZh485WdPXO/wmeeGy1iFi5sFC3oshiAkSTSb3NsusK8dOqOnT7/DCbBFQUjg/7uLXDcVdOteH4N1044jqH2kMdOBRFbRwaPJMQeB3UHu7AnzXB0ujJtOEwrBBR3BtMV3WkwBBcV2K4JhnGQvd68NJoAHi36WtYLSJW//hSfHrIhSun2tTzEXy+vjNxHDbVHsGkLCvuKJsMALrLf720TL3vpRvrddVStcoLbCgvsKG2xYVHf9vIVT8jQECg/o+290th9GTacBhWiChpBX9wRqorESuTDIeDsjT6hY++wpt/cQIIfLNWVkopc2uU87F4jl13W+3EZAC68+Ps9OjmqPT1bd3hcuOuDVyePFIEIOy5Di4aFys4wZqIqFe4eSxA6D5FiSbPlo6/q5iK1N6thILrxwD68xEt7X5Okb6tO1xurKtpwereVUJaKaKA4n72UaKB66v4n88fuiooFrBnhYioVyzVlRhuwcNdeVnpeHZhNs6l5yAva1RICf/BnI/+eqUcLjcWrqkJ2VfJIgq4d94U3FE2GW2dHtz2cu3gHyjp9FelWFscMZYwrBAR9Ur0IR9FuOGu3IxUTBhtRklJLkRR1BW+C96vaCC0exgFL4uta+0ICSplU7Kw4rpCTMywoq61A66z3UPymCkgXFAxCYBfRkhxxFjCsEJEpBELE1+HW7jhrkUlObrraEPGhQ4LRJoLZM+whrbtcAfueLkWZtGEHilQ2ybSjtc0NEQBePyGmbol/7GygaGCYYWIKMlEO9w1VBvZRappEykE+QH0SIFw0uXz48nKmTjiOofX6iJvJ0CD5/UH9r3SzkmKlQ0MFQwrRERJJtxwlyRJIdcbqo3sIoUj7fFUswk+yR9SadUiCjCbBAaVYfbKnw7D55d7a+RMj5kNDBUMK0RESSia4a6hmnDcVzXfqiWl6v5MX3/TFVLN1ivJ+Ld394a5VxoqoiCoy5iVkBJrE80ZVoiIKKyhnHAcLhyF25/pjfvLsap6LxqdZ9TrsfTK8LGIAp5eXKzugJ1mNqGyKAeVRTmcs0JERPFhOCccVze3hww3LJ5jx42zc3RhhYbHraWT8ND8aWjr9Kg9K0ouDN700+jgwqJwREQ04hwuN57dfkD9WbujdWVRDlLN/HgabpnpFrR1enSVg5X9rxTKJOuVv23E9c99DIfLbUhb+WwgIqIRp90gEgCWLyjUzWVZelW+QS1LHi/VHMKdr9TqKgebTQIOnvgW62pa1B6VcFWdRxqHgYiIaMQFT96tLDpf58XhcmPjzlbjGpdEtKuvLKIAyDJeqjkEAFiz/QA2Li2Licm2DCtERDTi+pq8G66yLQ2vm2bn4FL7OKyq3qce6/L54ez0xERVZ4YVIiIyRKTJu9pel3CbKtLQu9Q+DpVFOXh2+wF1eE6ZRxQLVZ0ZVoiIKKZoe13OuHvwL1tD66yYhcAQBmNM9FJEAZIfkGT9WbOIglpqf/vyClQ3twOArvy+0RhWiIgo5igfkt9/dkfYy31MKQNiEoDf3DMXEzOsqG5uV3tQgjcvzLOl44GKAoNbG4phhYiIYlJdaweHgIaIXwb+p7ENl03OjMmib/1hWCEiophkz7ByzsoQerXOgVfrHEg1m7B9eQUWz7Eb3aSosc4KERHFHKUUv1eSYREF3FmWZ3STEka3z6/OS4kXDCtERBRztMXIvJKMMVZzoA4IDYlOt9foJgwIwwoREcUcZfkyEFhCu+GTw/BKMswmAf940yVqcDGbBH6QDUJGusXoJgwI/8ZERBRzlOXLT99cjCVX5aOnd96Kzy/jM0cnnl5cDIsowOeXkWI2ocQ+zuAWx4+U3qXK8YQTbImIKCYpxcjW1bTojm9tasf7X7RDKXLb5fMjNzMdDdypOaIUUcC986YiI90SU/VTosWeFSIiimmVRTlIC9qFWVuNP9VswuV5GeCMlsgeXTgDt5flwTY61eimDAp7VoiIKKbl2dKxrbey6jPb9qtDQop502xhq9xSgEUUMGFsGq5/7mN1Q8L3l10NAHFTa4VhhYiIYprD5UZda4c6z0K72R4A/HHfSSOaFdNEQcDfzZ+KdR8fgleSsXJLo1qvxuOVUN3cjuc++EoXXmI5sDCsEBFRzHK43LoegaolpUg1m9TN9swCS++HI8ky1tUcgtcfODlKvRqvJKurrJSl4R6vhLrWDoYVIiKiwdDWW/F4JTg7Pdi+vAKv1R3B0Q4PFs66GI//7nN0aSexEADA69cHlKolpXB2elCWnwUAup4V5VisYlghIqKYpdRbCf5Q/fWnR+DxSvhg79eQe3cRThEF3DxnEl6vc4DRJeDeeVMw7aIxYeelKDtbc84KERHRBVDqrWg/VLfsdqq9Ld2aHpUeScabu4/Cj8Ck0tK8THx6uMOglhvPYgLuKJscMYgoS8PjAcMKERHFtOAPVW1vS6rZBAGBWivaTQ+9koxdrYkdVExA2B6kqdmjsPA7F/cZVOINwwoREcWV4N4WIDC3xZ5hxdKN9fB4paTYrfl/XVOgrvbRurV0Eh6oKDCoVcODYYWIiOJOcG+L8m8lxNgzrFhSVZfQE2+VoGI2ASbBhB7JjzSzKe5K6UeDYYWIiBKGNsRs6101tL53E8R4FW64R9tz5PMDT1YWwjY6NS4myw4GwwoREcUdpVBcXx/OebZ0PFF5Ce4om4y61g5YTAK2ffk1JmVZMb/wIjz7wQHUxcEEXGXCsFeSkWo2YcWCQkwYm4ZHNjeo1ym2Z6C8wGZYG4cbwwoREcWV4EJx/VVf1fa2/M1luerxFSjEbS/Xhr2NAGAk+2JyR4s4flaCFOHypxcXw+uXdSuitJydnuFvpIG4kSEREcWV4EJxdYNc9VNeYMMb95fjptk5MJv02yA+UDE15NhwunaKFfddnR/xcq9fxuI5djV0KSuiAKj1ZxwuN7bsdsLhco9Ek0cUe1aIiCiuRCoUpx0aAqLbpK+8wIbyAhtqW1y4a8MutdprZnoKfP4L61sxCUA0d2E2CciymrDuU0fYy1PNJl2FWeVxBlekHUhvU7xhWCEiorgSrlCcdmhIW3sl2g/u8gIbPlwxX73PtgsYVinIHoXyqTZs+cypK1oXic8v44X6bxBpDvCKBYVq+yMNgWkL5cXDXj8DZWhYufbaa3Hs2DHdsfvvvx8rV640qEVERBQPgpcua4eGtAFhIB/c2vusbm4fdNucnR7k2dLDBpUUUYDPL4f0uEiyfhKt5PfD5w8M8WiXIocbAsuzpUfsbUoUhvesPPzww7jlllvUn9PTEycJEhHRyIhU1XY4PrgtJmDhd3KwcNbFeOx3n6Pb54coQO0ZUUKKdndoxaMLZ6DYnqEOOWndc2U+skanAgAmjE3Dp4dcWFSSG7F6r/axhettSiSGh5VRo0Zh/PjxRjeDiIjiWKSqtoP94K4sysGa7QdCisrdWjoJD82fpt7nZXmZIdVztb0hq6r3qbe1iAIqi3KQZ0vHhyvmo7q5Hc9s248eSUaKCbi6MBv3/eYztecEAN5paNMNY/UVSuJpr5+BMjysvPLKK1i7di0mTJiAG264Affeey9SUlIGfD+SFGnBV3xSHs+FPi5Hhxv1radRmp+JvKzEfBIPtaE69zRwPPfGSYRzn5uRikUl54dMlH8P5jHlZqSi+pF5eK/5a/z7h1+pvTQPXj0FuRmp6n1qf+e7D1+F+tbTyM1IQ+2hUyiaOEbtBbGIAjYuuUK9bW5GKu6bl4+Fsy7CrkMujOn6Gkc73LqgAgSGemoPnUJuRq6ubRfy2GLFQNouyMre2gbYuHEjZs2ahbFjx6KpqQnPPPMMvv/97+Pf/u3for4PSZLQ0NAwfI2MY8fP+rBi2yl0S0CqCDy7MBsTRhueT4mI4sLxsz7sPeXF+HQTTrr9uCTb0u97aPD77j/MyxzUbRXJ8N5dUlICURT7vM6QP/rnn38eL7zwQp/X2bJlC2bPno0lS5aox2bOnImxY8fi4YcfxsqVK5GZmTmg3zt79ux+H2w8kSQJTU1NF/S4fvfZMXRLpwAA3RJwLj0HJSW5/dyKhuLc0+Dw3BuH517P0eHGT361U50Ds+y6aZg1a0K/PdTB77vWbDuWX973+65y7hd89zK8N6tb7Z051tmV0L3iyuOOxpCHlTvvvBM33nhjn9ex2+1hj5eUlAAAHA7HgMOKKIoJ+QK7kMdVPjVbNxGrfGp2Qp6j4ZKoz6l4wHNvHJ77gN2OM7rVRavfO4BffdjS7zLoC3nfFUURU8aPwZTxY4bkMSSSIQ8rWVlZyMoa3MzrL7/8EgA44XaIjOTs8Gj26SAiihfaVTeKaJZBJ/qqHKMYNgi2Z88eNDY2Yu7cuRg9ejSampqwatUqXHvttZg4caJRzYpJFxIELmR2eLS/d6D7dBARxToldFQ3t6urgqJdBp3Iq3KMYlhYSUlJwbvvvosXXngBPT09mDhxIm655Rbcd999RjUpJjk63Lixd9w0OAgMZ2/GQAJIpCJF0fwOfvsgoliVZ0vHAxUFqCzK4XuVwQwLK9/5znfw5ptvGvXr40Z96+mwQWC4ezMGEkAGUzmRvTFEFC/YU2K8xF0LlSBK8zPDBoHB9mZo9dWzMZAAMpgx2qFoPxERJQeGlRiXlxU+CFzoPhDBO4wG92wMNIAM9JtHou9jQUREQ4dhJQ6ECwJ9hYn+tkl3uNy6fSk8Xgkv7jioKyEd6feGM5i5J5wxT0RE0WJYiTPBwUCZv7Jlt1MNJ8pckDSzCTICNQK0vSd1rR0hG2htrj+q7kEBRL+nxoXMPeE4MBERRYNhJY6ECwYAdMeWXTddnQvSFWGbdO0QjGgSIPnP97BUN7fjuQ++Uvey2HTPXJQX2CL21nDuCRERDTeGlRjQ3zCKcrnrbHdIMFD+rfy/0+2FRRTgleSQnhXtVuJVS0rxVsMxXDnVhid+36SGnU63V70/ryTjrvW7sOneuepuotqt19PMJvz4cn01YotJUHt5GFqIiGgoMKwYLFJvSe2hUxjl9unqrKSZTUg1m0LCh9JLkmY2YcPOw/BKcmCHz6VlAIC3Go5hUUmuGh7+e88xrPhtIyS/jP/ecwxLrspHZnoKiu0Z+GlVna59Xr+MTbVHdGWnFV0+P16tc+iuv+LNBkgyoh4SYq0VIiLqD8OKwYKHUbTDMCkicN3RA7phnZtm5+BS+zhUFuWoH+7KRNWDJ77FSzWHAAR6RRqdnXh2+wF0+/x4e88xbF9egbZODx7Z3KD+/i6fHy/VHILZBHxv+nhdGFFMyrKqgUjbsxKOMhVGeSy20al99hix1goREfWHYWUEhetFCF7CC5wf1umRgHebj+vuY2tTO/647wQqi3JQ2+JSe03K8rPwv986v3ulAOCLY2fU8NHt8+O1uiM42uEJ2zafH/ho/8mQ4ymiAAECfnrlZLSd9uBIhxuX2sdhx/6TOHo6/H0BgNkk4Jfv74PPr+9l0Z4DznchIqJoMKyMkEi9CMFLeAGoPStaZVOyUHf4/ByV1+qOqL0om+uP4o6ySbreDhnAO5+36+5jXc0hiEL0bZ6UacXX33RjbU2L7nij84zuZ4sowCfJUNYXmQRA8p//WellqSzK0Z2DqiWlrLVCRET9MhndgGQRrhdBoazQUY5VLSmFRZMqUkQB08eP1t3f/uPf6n5+ve5o2N+rzSYyAJ8c9mphHT3tQY8UfrhHMX5Mii6oAIBfBoJ/zf97fz8e29KoOwfOTg/eX3Y1nr65mENAREQUEXtWRkhfFVuDe12WXTddVwdFlhEykfX0uR7dz5EyyACyyaCc/Lan/ysh0NNSe/h8QEs1m3S1YoJph7jKC2xD1l4iIoo/DCsjpK+KrcG9LsD5FT7KMuRgDUFDMfHmnqumoLo5MEylnSwMBILKbS/XAggMcb1xfzkDCxFREmNYGUGRehGCe12K7Rm4uzwPTYfbcPN3C7FySxPC5JW4pp0H88y2/fhgxXz13GyqPaK77qbaIwwrRERJjGElBmh7XewZVvy0qk5dxVP/++aECyrBeiQZr9UdwR1lk1HX2gFR0M8CHmfl05SIKJnxUyDG7DhwQlfrJNwQUCJaV3MIGz45jB5Jhjlo2vdk2yjdzywkR0SUXBhWhslAPlBrW1y6XZCTkYxADwsQqPkiCoECc6lmEyqLctTrsZAcEVHyYVgZBtF+oDpcblQ3t6vF0+g8kyDgsRtmhEy+ZSE5IqLkw7AyDCLVVNH2tGgDTX8EDP8S5Fjj9cs47e4JCSL2DGufPxMRUeJhWBkGwat77BnWkMqt2s0Bg+VlWuHQlLJPtqCi0G4NoN15WsvZGbnkPxERJQaGlT4MdCKn9vramirBPS0/WV+rG/axiAL8flld9dPXnjvJZOGsiwHoh9VSzSaYTVD3HGKJfiKixMewEsFAJ3KGu/7iOXYAQFunR/2ABRAyP8UnyZgwLg3tZ7oAJG9PSjCvP3Amqpvb1bCnrJSyiAKqlpRyvgoRURLg3kAR9LWXz0Cu73C5sXRjfZ8TaGVADSp0nj3DCofLjWe3Hwi5zCvJHAIiIkoS7FmJoK+9fKK9vsPlxos7DkY1iZZCOTs9cHZ6dHVnOARERJR8GFYi6Gsvn2iuDwAL19SgS/NBawLAFcrR++xIB+ZO0ZfZf+bmEnj9MgvCERElEYaVPkTayyea66+radEFlZtm52DhrIvxyOaGoW5mwnqt7ijeqDuqO7bv+LeQIeOjfSdwV/lk7hlERJQEGFZG0MVj03BnWR7+uP8E56hEKbgn6qWaFnUC8tamdu7ITESUBBhWhpiyfHnC2DSYTQJ8vStatja1Y2tTu8Gti3/BK6XeajjGsEJElOAYVoZQuKq0okmA5Odi5KESXM238KLR2LLbyTksREQJjGFlCGmXLyskvwyLKCT1JoVDSYY+AP7L1r0AwE0NiYgSGOusDCF7hhUWUQg5/sDVUzFzwhjdscvzxo1UsxJOuJ4qj1dCdTOH2YiIEhHDyhBRir95JRnBeeWFj1qw7/i3umOfOc6MYOuSw7PbD8DhchvdDCIiGmIMK0NEOwQkyYHiZTSyun3+fisNExFR/OFH6hBwuNw4eELfc3LrFXkGtSZ5aSsHb9ntZC8LEVGC4ATbCxRuBRAQKBDHibXDQxCAv549Ee983qYeu7V0EhaV5KK6uR1rth9Al8/PSbdERAmCYaUPSs2UvpbFhlsBZLWIqCzKwRHXObwWVIGVLpwsA+82tyPNbEKXzw+LKODKqTYs3Viv+1soG0oyrBARxTeGlQi0PSZ9fUPXbmCYIgpYMGsC7iqfjDxbOsZaLQa0PDn4/DK+Nz0bnxw8Ba8kY+WWxpBeLG52SESUGBhWItD2mPT1DV3ZwFAZftja1I73mo/jptkTuJR2iE2/aBQOn3KrVYE/2n9SvcwryWrF4FSzCSsWFKKyKIe9KkRECYBhJQJtj0l/39DzbOmwjU5VNy6UZBnvfM6gMtQun5yF9T8tw4s7DmJzfejwmkkAnqycyZBCRJRgGFYiUHpM+puzorBnWEeoZclrUUku8mzpeGj+NPz+M2fIsE+PJMM2OpVBhYgowXDpch/ybOlYPMce1Yefs9MzAi1KXv9+awnKC2zqpOenFxeHVAvmHBUiosTEnpUhoh02oqH3dsMx7D3+DTbubFVXAD29uBhevwx7hhXOTg83MyQiSlDsWRkiebZ0VC0pDbs3EF24j/afxEs1h9R5QcoKoLL8LJQX2KLuASMiovjDsDKEnJ0e3TyKa2aMh9nE8DJcvJKM1+qOGN0MIiIaZgwrQ8ThcsN1thupvZsCWS0ifvGDIvzx0fm4ZsZ4g1uXuF6qOYT/3nPM6GYQEdEw4pyVIaAtIJdmNumWz9a2uFBz4GT/d0KDtuK3jbgsL5PDQERECYo9K0OgurldnVjb5fOj0+1Fni0dDpcbP1m/C35uDzSsJL/M3ZaJiBIYe1YukMPlxjPbDuiOra1pQUXheDg7PWq1VRo+XLJMRJTYGFYuUHVzO3okf8jxTbVHcKl9HCwmAV4GlmFhNgF/fz0r1hIRJTqGlQt02t0T9vgHe7/G1qZ2cCXz8BAF4L/uLUd5gc3ophAR0TDjnJUL4HC5UbWzVXdMAHBnWR661X2CRr5diU4UgFfvY1AhIkoWDCsXoK61Qw0lChmBAnEp7FIZMpnpFt3Pj90wM2JQcbjc2LLbCYfLPRJNIyKiEcBhoAsQrsS+1SKi2J4BdqgMncm2dLh7vkW3zw+rRURlUU7Y62mXkFstIt5fdjXnshARJQCGlQug3ZlZ2Z/GnmHFWw3HQnYEpsFrOHompH5NOHWtHWpw9Hgl1LV2qEvIo909m4iIYg/DygXKs6WrH4Dab/Y0tLo0w21bdjvDBg9tT5eynJm9LURE8Y9hZQhpv9kDgGgSIIVZtiwKnHg7GM9uP4Bntx9Qh4OCg4e2p0sJM1t2O8P2thARUfxgWBlCwd/sq5aUwtnpgcUkYMPOw2h0ngEQCComAKHVWShY+ZQs1B4OVKfVTmaOFDy0PV1A+N4WIiKKLwwrQyjcN/tIQ0OX2sehoTe8UHgpooDPHKfVn5VNIrt9fqSZTXCd7YbD5e6zpyTc34SIiOILw8oQC/5mHzw0pGBQ6d9V07Lx0f7zm0AuvSofmekpOO3uwYZPDmNV9T48u/0Ati+v6DewMKQQEcUvhpVhoF19UpafhTSzCV0+P8wmgXsFDcCMCWPw5xYXunx+pIgCNu5s7T2PgDIi1O3zo7q5HQ9UFBjbWCIiGjYMK0MsePVJ1ZJSteaKSYAaXKhvAoC20x745cDZ88tQ92Di6SMiSi4MK0MsuNbHWw3H1ImhPZKMJytnwDY6FfYMKzbVHsHWpnYjmxtzbOkWuNxeyADe+fz8ufH55bA9U2lmU8QicURElBhYbn+IKatPgEA120UlubqfK4tysHiOHRMzrPhg79e621pYoh8utzfs8cDkWn1QubV0Erb1M1+FiIjiH3tWhli41SfhVqNUN7frluJ+d0oWdvUu0aXzLCZg5fUzAQCrqvedPy4KeGj+NAYVIqIkMKxhZe3ataipqcHevXthsVjwl7/8JeQ6bW1t+D//5/+gtrYWqamp+Ou//ms89thjSElJGc6mDavg1SfhVqOcdvfofpaRHHVXZk0Ygy+Pf9vv9UQh0HPyYEUgkNS2uGARBXglGaIAPL24mEGFiChJDOswkNfrxQ033IDbb7897OWSJOGBBx6A2+3Ga6+9hjVr1uD999/H6tWrh7NZMSEzXR/GrCmiQS0ZOWaTgP1f9x9UgEDhvMsnn69Vs3RjvbrfkiQDT/y+iTsrExEliWENKw8//DCWLFmCwsLCsJd/8sknOHjwIH75y19i1qxZuPLKK/HEE0/gzTffxNmzZ4ezaYZxuNzYstuJCWPTdMd/WJKLlASfs+Lzy7ptBgqyR+kunzlhjHoOtNVmw9WqUSrYEhFR4jN0zkpDQwOmT5+Oiy++WD02b9489PT0oLm5GeXl5VHflyTF/uaBjg43bvzVTni8Ushk2rYzbpgEAYAMiwnwasaEJmem4cjprpFt7Ag4etqNFFFAT2+C2Xf8W6SIAh6/fgZuKLoYuRmpkCQJc/LGqSXzFVaLiDl544bl767cZzw8pxINz71xeO6Nk6znfiCP19CwcurUKWRnZ+uOjRs3DhaLBadOnRrQfTU1NQ1l04bFR60e9QPXK8kwC4BPBlJFoO1Yu1p/xesH5tlTcKBDwqSxJswab0YtzPjqtM/I5g+5HknGlfY0fOrs0h0713EcHY4z+PJLH/ae8uKSbAuevi4Te095MT7dhJNuPy7JtqDDcQAdjuFrXzw8pxIVz71xeO6Nw3Mf2YDDyvPPP48XXnihz+ts2bIFs2fPjur+BCH80Eek45HMnj0bohjb8z6y8txY37BTLRj3yt2X41hnF0rzMwEAW/YFLkszm1DX7kWPJOOEW8Lu4964XtY8c8JopJhFfB60xUCq2YSHrp+Nz369Ww1qqWYTfnx1MQDgJ786f67effgq3JA1MhNqJUlCU1NTXDynEg3PvXF47o2TrOdeedzRGHBYufPOO3HjjTf2eR273R7VfWVnZ6OxsVF37MyZM/B6vbDZbANqlyiKMf9HnjJ+TJ+b6imXuc5265bpAlAnl8ajgyfOhd1mYMWCQlw1/SJsW16B6uZAATilwNuLOw7qiuvtdpzBlPFjRq7RiI/nVKLiuTcOz71xeO4jG3BYycrKQlZW1pD88pKSErz00ks4ceIELrroIgDAzp07kZKSgqKioiH5HbGmr031lMscLjfWbD8QUpZfO78jnkTaD+m0u0fdNVnZ2yfcLtXaybZERJR8hnU1UFtbG/bu3Yu2tjZIkoS9e/di7969OHfuHIDAZNpp06bhsccew5dffok///nPWL16NW655RaMHj16OJsW0/Js6ah+ZB6mZ+qz5D3zpuDpm4tRPiXyB3csDBaZTdG14qWaQ7j+uY91S5CDV/7cWjoJ7y+7mjVViIiS2LCGlV/96lf44Q9/iOeffx5utxs//OEP8cMf/hDNzc0AAl1e69atQ2pqKm6//XYsW7YM1113HR5//PHhbFZcaOv0hEyoFSBg8Rw7ll0Xfik4AAxwqs+Qu7V0Ev7r3rkhc2xuLZ2Ef7+1JOR48BLk4O0KWKWWiIiGdTXQU089haeeeqrP60ycOBHr1q0bzmbEpf9uDN3gcMPOw7i9LA/lBTY8WDEVL9Uc0l0uCoCRo0QmAVhUkovyAhs23TMXd23YBa8k60LHZXmZqG5ux7PbD6Db5w8Z4om0PQERESUv7g0Uo/6mOAdv/sWpO9bt86OutQN5tnTcUTYZL//pMCTNfJCrC8fj0xaXbs+haJkQudx/uN2Ow/HLwJKqOmxbXoHyAhs+XDE/JHQo81Mqi3IiBpK+5vUQEVHyYViJUeVTbfhFRSZ2daTggy9PoKe3h0LphcizpePZm4vxyOYG9TbzpmXjT1+d1N1PoMxc30RBwLO3FMPrl9F66iy2Nh3HVNsofLj/BIDABFmzCdBmoOCfFV2aQBXNZOLBcrjc7H0hIkoSDCsxrOiiVPxkYQmOdXaH/WD+m8tycfHYNLzVcAxXTrVh5ZZGXYC4tXQSMtMtuuEiE4Cf33QJnnpvn2avHRlP/L4JVUtKAQC/XlqGtk6PGlYAqNV1U0QTFsy6GAtnXYzHfvd5SC+OxSTAnmEd1OONNoBoVwxZLSIn4BIRJTiGlTjQVy9EeYENEzOseHHHQV0tFosoYFFJLhqdnbpeED+Acekp+HDFfLy44yA21x8FEJjoqp1jsuy66brfoyyZ7pH82NrUjj/uO4FfLy2Ds9MDe4YVOw6cwPpPDsMryVi6sX7AAWIgAUS7YkiZoMuwQkSUuBhW4ly4uiQWUcDTi4uxdGM9PF4JKaLQG1jODyXl2dLx0PxpeKehTd2rSAk7Hq+ETrdX93uCJ+96vBKcnR4snhMoAOjs9OhuP9AAMZAAoqwYUoINa7AQESU2hpU4EzxUEq4uyaKSXLzVcEw93iPJeLJyJmyjU0Mmuyorb+wZVjXcWC0iMtItut8ryYEQJPTeX3BIuNAAMZDbc8UQEVFyYViJI+GGSoI/5BeV5KqhQ2G1iKgsygn7oa4dYtIGAAB47oOvdPfjjRB6lPu5kAAx0NtzxRARUfJgWIkj4YZKFs+x6z7kw/W0RFtYLTgAvL/salQ3t6ul/60WEcX2DDg7PVHdfqAYQIiIKByGlTgSaagk+ENee50LqQAbXBMleKiIq3CIiGgkMKzEkWiGSoZjPocShrbsdnIVDhERjTiGlTgTzVDJcA2ncBUOEREZgWGFosZVOEREZASGFRoQToIlIqKRZjK6AURERER9YVghIiKimMawQkRERDGNYYWIiIhiGsMKERERxTSGFSIiIoppDCtEREQU0xhWiIiIKKYxrBAREVFMY1ghIiKimMawQkRERDGNYYWIiIhiWtxvZCjLMgBAkiSDWzK0lMeTaI8rHvDcG4fn3jg898ZJ1nOvPF7lc7wvghzNtWJYT08PmpqajG4GERERDcLs2bORkpLS53XiPqz4/X74fD6YTCYIgmB0c4iIiCgKsizD7/fDbDbDZOp7VkrchxUiIiJKbJxgS0RERDGNYYWIiIhiGsMKERERxTSGFSIiIoppDCtEREQU0xhWiIiIKKYxrBAREVFMY1ghIiKimMawEoPWrl2L2267DcXFxbjiiivCXqetrQ0PPvggSkpKMHfuXPzrv/4renp6Rrilie/aa6/FjBkzdP89/fTTRjcrIb366qu49tprMXv2bPzoRz/CX/7yF6OblPCef/75kOf3VVddZXSzElJ9fT0efPBBzJs3DzNmzMAHH3ygu1yWZTz//POYN28eLr30Utx111346quvDGpt7In7jQwTkdfrxQ033ICSkhJs2bIl5HJJkvDAAw8gMzMTr732Gjo7O/H4449DlmX84z/+owEtTmwPP/wwbrnlFvXn9PR0A1uTmN59912sWrUK//zP/4zLL78cb7zxBu6//35s3boVEydONLp5CW369OmoqqpSfxZF0cDWJC63240ZM2bgRz/6EX72s5+FXP7yyy+jqqoKTz31FPLz87F27VosXboU7733HkaPHm1Ai2MLw0oMevjhhwEAv//978Ne/sknn+DgwYPYsWMHLr74YgDAE088gSeeeALLly/nE3uIjRo1CuPHjze6GQmtqqoKP/7xj3HzzTcDAH7+85/jk08+weuvv45HH33U4NYlNlEU+fweARUVFaioqAh7mSzL+M1vfoMHH3wQCxcuBACsXr0aV155Jf7whz/gtttuG8mmxiQOA8WhhoYGTJ8+XQ0qADBv3jz09PSgubnZwJYlpldeeQVz587F3/zN32Dt2rUcbhtiPT09+OKLLzBv3jzd8auuugp79uwxqFXJ48iRI5g3bx6uvfZaLF++HEePHjW6SUnH6XTi5MmTutdASkoKSktL+RroxZ6VOHTq1ClkZ2frjo0bNw4WiwWnTp0yqFWJ6e6778asWbMwduxYNDU14ZlnnoHT6cS//du/Gd20hHH69GlIkgSbzaY7np2djZMnTxrUquRw6aWXYvXq1cjPz4fL5VLny/3hD39AZmam0c1LGsrzPNxroK2tzYgmxRyGlRHy/PPP44UXXujzOlu2bMHs2bOjuj9BEAZ0nM4byN9iyZIl6rGZM2di7NixePjhh7Fy5Uq+mQ+x4OeuLMt8Pg+z4GGJkpISLFiwAG+//TaWLl1qUKuSV7jXAAUwrIyQO++8EzfeeGOf17Hb7VHdV3Z2NhobG3XHzpw5A6/XG5LMKdSF/C1KSkoAAA6Hg2FliGRmZkIUxZBeQZfLFdKDSMMrPT0dhYWFaG1tNbopSUWZM3Tq1ClcdNFF6nG+Bs5jWBkhWVlZyMrKGpL7KikpwUsvvYQTJ06oT+ydO3ciJSUFRUVFQ/I7EtmF/C2+/PJLAOCExCGUkpKC73znO9i5cycWLFigHv/000/x/e9/38CWJZ+enh60tLRgzpw5RjclqdjtdowfPx47d+7ErFmzAAT+FvX19Vi5cqXBrYsNDCsxqK2tDWfOnEFbWxskScLevXsBAHl5eRg1ahTmzZuHadOm4bHHHsNjjz2GM2fOYPXq1bjlllu4EmgI7dmzB42NjZg7dy5Gjx6NpqYmrFq1Ctdeey2X0w6xpUuX4rHHHkNRUREuu+wybN68Ge3t7VwFMcxWr16Na665Bjk5Oejo6MDatWtx9uxZLFq0yOimJZxz587B4XCoPzudTuzduxfjxo3DxIkTcffdd2PdunXIz8/H5MmTsW7dOqSlpeGv/uqvDGx17BBkDorFnCeeeAJvvfVWyPHf/OY3mDt3LoBAoPnFL36B2tpa9Qn9+OOPIyUlZaSbm7C++OIL/OIXv8ChQ4fQ09ODiRMn4qabbsJ9990Hq9VqdPMSzquvvor169fjxIkTKCwsxJNPPonS0lKjm5XQli9fjvr6enR2diIzMxMlJSV45JFHMG3aNKOblnB27dqFu+++O+T4okWL8NRTT0GWZbzwwgvYvHkzzpw5g+LiYvzTP/0TCgsLDWht7GFYISIiopjGOitEREQU0xhWiIiIKKYxrBAREVFMY1ghIiKimMawQkRERDGNYYWIiIhiGsMKERERxTSGFSIiIoppDCtEREQU0xhWiIiIKKYxrBAREVFMY1ghIiKimPb/A+xfO+ZQW21wAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n, d, k = 200000, 2, 8\n",
    "\n",
    "X, _ = make_blobs(n_samples=n, n_features=d, centers=k, cluster_std=0.75, random_state=0)\n",
    "\n",
    "plt.scatter(*X[:,:2].T, s=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "236be605",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Exception ignored on calling ctypes callback function: <function _ThreadpoolInfo._find_modules_with_dl_iterate_phdr.<locals>.match_module_callback at 0x7f0b0f857ee0>\n",
      "Traceback (most recent call last):\n",
      "  File \"/home/jmschr/anaconda3/lib/python3.9/site-packages/threadpoolctl.py\", line 400, in match_module_callback\n",
      "    self._make_module_from_path(filepath)\n",
      "  File \"/home/jmschr/anaconda3/lib/python3.9/site-packages/threadpoolctl.py\", line 515, in _make_module_from_path\n",
      "    module = module_class(filepath, prefix, user_api, internal_api)\n",
      "  File \"/home/jmschr/anaconda3/lib/python3.9/site-packages/threadpoolctl.py\", line 606, in __init__\n",
      "    self.version = self.get_version()\n",
      "  File \"/home/jmschr/anaconda3/lib/python3.9/site-packages/threadpoolctl.py\", line 646, in get_version\n",
      "    config = get_config().split()\n",
      "AttributeError: 'NoneType' object has no attribute 'split'\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.47 s ± 0 ns per loop (mean ± std. dev. of 1 run, 1 loop each)\n",
      "1.38 s ± 0 ns per loop (mean ± std. dev. of 1 run, 1 loop each)\n"
     ]
    }
   ],
   "source": [
    "means = X[numpy.random.choice(X.shape[0], replace=False, size=k)]\n",
    "means2 = numpy.copy(means)\n",
    "\n",
    "covs = numpy.array([numpy.eye(d) for i in range(k)])\n",
    "covs2 = numpy.copy(covs)\n",
    "\n",
    "priors = numpy.ones(k) / k\n",
    "\n",
    "%timeit -n 1 -r 1 GaussianMixture(k, tol=1e-2, max_iter=20, means_init=means, precisions_init=covs, weights_init=priors).fit(X)\n",
    "%timeit -n 1 -r 1 GeneralMixtureModel([Normal(means2[i], covs2[i]) for i in range(k)], tol=1e-2, max_iter=20, init='random').fit(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "54316b85",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Exception ignored on calling ctypes callback function: <function _ThreadpoolInfo._find_modules_with_dl_iterate_phdr.<locals>.match_module_callback at 0x7f0b3c27e4c0>\n",
      "Traceback (most recent call last):\n",
      "  File \"/home/jmschr/anaconda3/lib/python3.9/site-packages/threadpoolctl.py\", line 400, in match_module_callback\n",
      "    self._make_module_from_path(filepath)\n",
      "  File \"/home/jmschr/anaconda3/lib/python3.9/site-packages/threadpoolctl.py\", line 515, in _make_module_from_path\n",
      "    module = module_class(filepath, prefix, user_api, internal_api)\n",
      "  File \"/home/jmschr/anaconda3/lib/python3.9/site-packages/threadpoolctl.py\", line 606, in __init__\n",
      "    self.version = self.get_version()\n",
      "  File \"/home/jmschr/anaconda3/lib/python3.9/site-packages/threadpoolctl.py\", line 646, in get_version\n",
      "    config = get_config().split()\n",
      "AttributeError: 'NoneType' object has no attribute 'split'\n"
     ]
    }
   ],
   "source": [
    "means = X[numpy.random.choice(X.shape[0], replace=False, size=k)]\n",
    "means2 = numpy.copy(means)\n",
    "\n",
    "covs = numpy.array([numpy.eye(d) for i in range(k)])\n",
    "covs2 = numpy.copy(covs)\n",
    "\n",
    "priors = numpy.ones(k) / k\n",
    "\n",
    "model_sklearn = GaussianMixture(k, tol=1e-2, max_iter=20, means_init=means, precisions_init=covs, weights_init=priors).fit(X)\n",
    "model_pom = GeneralMixtureModel([Normal(means[i], covs[i]) for i in range(k)], tol=1e-2, max_iter=20).fit(X)\n",
    "\n",
    "y_hat_sklearn = model_sklearn.predict(X)\n",
    "y_hat_pom = model_pom.predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "7d4dc4bb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1400x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(14, 5))\n",
    "\n",
    "plt.subplot(121)\n",
    "for i in range(k):\n",
    "    plt.scatter(*X[y_hat_sklearn == i].T, s=3)\n",
    "    plt.scatter([model_sklearn.means_[i, 0]], [model_sklearn.means_[i, 1]])\n",
    "\n",
    "plt.subplot(122)\n",
    "for i in range(k):\n",
    "    plt.scatter(*X[y_hat_pom == i].T, s=3)\n",
    "    plt.scatter([model_pom.distributions[i].means[0]], [model_pom.distributions[i].means[1]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "5e4e5bf9",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Exception ignored on calling ctypes callback function: <function _ThreadpoolInfo._find_modules_with_dl_iterate_phdr.<locals>.match_module_callback at 0x7f0b0f8afd30>\n",
      "Traceback (most recent call last):\n",
      "  File \"/home/jmschr/anaconda3/lib/python3.9/site-packages/threadpoolctl.py\", line 400, in match_module_callback\n",
      "    self._make_module_from_path(filepath)\n",
      "  File \"/home/jmschr/anaconda3/lib/python3.9/site-packages/threadpoolctl.py\", line 515, in _make_module_from_path\n",
      "    module = module_class(filepath, prefix, user_api, internal_api)\n",
      "  File \"/home/jmschr/anaconda3/lib/python3.9/site-packages/threadpoolctl.py\", line 606, in __init__\n",
      "    self.version = self.get_version()\n",
      "  File \"/home/jmschr/anaconda3/lib/python3.9/site-packages/threadpoolctl.py\", line 646, in get_version\n",
      "    config = get_config().split()\n",
      "AttributeError: 'NoneType' object has no attribute 'split'\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10.1 s ± 0 ns per loop (mean ± std. dev. of 1 run, 1 loop each)\n",
      "6.31 s ± 0 ns per loop (mean ± std. dev. of 1 run, 1 loop each)\n"
     ]
    }
   ],
   "source": [
    "n, d, k = 200000, 25, 8\n",
    "\n",
    "X, _ = make_blobs(n_samples=n, n_features=d, centers=k, cluster_std=0.75, random_state=0)\n",
    "\n",
    "means = X[numpy.random.choice(X.shape[0], replace=False, size=k)]\n",
    "means2 = numpy.copy(means)\n",
    "\n",
    "covs = numpy.array([numpy.eye(d) for i in range(k)])\n",
    "covs2 = numpy.copy(covs)\n",
    "\n",
    "priors = numpy.ones(k) / k\n",
    "\n",
    "%timeit -n 1 -r 1 GaussianMixture(k, tol=1e-2, max_iter=20, means_init=means, precisions_init=covs, weights_init=priors).fit(X)\n",
    "%timeit -n 1 -r 1 GeneralMixtureModel([Normal(means2[i], covs2[i]) for i in range(k)], tol=1e-2, max_iter=20, init='random').fit(X)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
